LTS Termination Proof

by AProVE

Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
l5 l5 l5: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l22 l22 l22: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l48 l48 l48: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l18 l18 l18: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l17 l17 l17: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l52 l52 l52: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l35 l35 l35: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l21 l21 l21: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l6 l6 l6: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l34 l34 l34: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l46 l46 l46: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l53 l53 l53: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l19 l19 l19: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l33 l33 l33: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l40 l40 l40: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l47 l47 l47: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l58 l58 l58: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l37 l37 l37: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l11 l11 l11: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l49 l49 l49: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l32 l32 l32: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l63 l63 l63: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l28 l28 l28: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l42 l42 l42: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l2 l2 l2: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l23 l23 l23: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l44 l44 l44: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l51 l51 l51: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l16 l16 l16: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l65 l65 l65: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l30 l30 l30: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l56 l56 l56: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l39 l39 l39: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l43 l43 l43: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l60 l60 l60: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l1 l1 l1: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l13 l13 l13: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l31 l31 l31: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l9 l9 l9: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l14 l14 l14: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l25 l25 l25: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l55 l55 l55: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l8 l8 l8: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l27 l27 l27: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l0 l0 l0: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l12 l12 l12: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l61 l61 l61: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l26 l26 l26: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l54 l54 l54: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l7 l7 l7: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l24 l24 l24: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l3 l3 l3: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l41 l41 l41: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l20 l20 l20: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l62 l62 l62: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l45 l45 l45: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l59 l59 l59: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l57 l57 l57: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l38 l38 l38: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l10 l10 l10: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l36 l36 l36: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l29 l29 l29: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l15 l15 l15: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l64 l64 l64: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
l50 l50 l50: x1 = x1x2 = x2x3 = x3x4 = x4x5 = x5x6 = x6x7 = x7x8 = x8x9 = x9x10 = x10x11 = x11x12 = x12x13 = x13x14 = x14x15 = x15x16 = x16x17 = x17x18 = x18x19 = x19x20 = x20x21 = x21x22 = x22x23 = x23x24 = x24x25 = x25x26 = x26x27 = x27x28 = x28x29 = x29x30 = x30x31 = x31x32 = x32x33 = x33x34 = x34x35 = x35x36 = x36x37 = x37x38 = x38x39 = x39x40 = x40x41 = x41
and for every transition t, a duplicate t is considered.

2 SCC Decomposition

We consider subproblems for each of the 3 SCC(s) of the program graph.

2.1 SCC Subproblem 1/3

Here we consider the SCC { l0, l2 }.

2.1.1 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by 0.

l0: −1 − x14 + x18
l2: −1 − x14 + x18

2.1.2 Transition Removal

We remove transition 3 using the following ranking functions, which are bounded by 0.

l2: 0
l0: −1

2.1.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.2 SCC Subproblem 2/3

Here we consider the SCC { l39, l38, l37, l36, l34, l31, l35 }.

2.2.1 Transition Removal

We remove transition 50 using the following ranking functions, which are bounded by 0.

l31: 2⋅x2 + x16
l35: −1 + 2⋅x2 + x16
l34: 2⋅x2 + x16
l39: 2⋅x3 + x17
l38: 2⋅x3 + x17
l37: 2⋅x3 + x17
l36: −1 + 2⋅x2 + x16

2.2.2 Transition Removal

We remove transitions 59, 58, 57, 56, 55, 54, 53, 52, 51 using the following ranking functions, which are bounded by 0.

l34: 0
l31: −1
l39: 1
l38: 2
l37: 3
l36: 4
l35: 5

2.2.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

2.3 SCC Subproblem 3/3

Here we consider the SCC { l7, l6, l10, l11, l8, l13, l12, l9 }.

2.3.1 Transition Removal

We remove transition 7 using the following ranking functions, which are bounded by 0.

l6: x2 + x5
l8: −1 + x2 + x5
l7: x2 + x5
l13: x7 + x8
l12: x7 + x8
l11: x7 + x8
l10: x7 + x8
l9: −1 + x2 + x5

2.3.2 Transition Removal

We remove transitions 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8 using the following ranking functions, which are bounded by 0.

l7: 0
l6: −1
l13: 1
l12: 2
l11: 3
l10: 4
l9: 5
l8: 6

2.3.3 Trivial Cooperation Program

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

Tool configuration

AProVE